Chris@16: /*
Chris@16:  [auto_generated]
Chris@16:  boost/numeric/odeint/stepper/modified_midpoint.hpp
Chris@16: 
Chris@16:  [begin_description]
Chris@16:  Modified midpoint method for the use in Burlish-Stoer stepper.
Chris@16:  [end_description]
Chris@16: 
Chris@101:  Copyright 2011-2013 Mario Mulansky
Chris@101:  Copyright 2011-2013 Karsten Ahnert
Chris@101:  Copyright 2012 Christoph Koke
Chris@16: 
Chris@16:  Distributed under the Boost Software License, Version 1.0.
Chris@16:  (See accompanying file LICENSE_1_0.txt or
Chris@16:  copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16:  */
Chris@16: 
Chris@16: 
Chris@16: #ifndef BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED
Chris@16: #define BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED
Chris@16: 
Chris@16: #include <vector>
Chris@16: 
Chris@16: #include <boost/numeric/odeint/stepper/base/explicit_stepper_base.hpp>
Chris@16: #include <boost/numeric/odeint/util/resizer.hpp>
Chris@16: #include <boost/numeric/odeint/util/is_resizeable.hpp>
Chris@16: #include <boost/numeric/odeint/algebra/range_algebra.hpp>
Chris@16: #include <boost/numeric/odeint/algebra/default_operations.hpp>
Chris@101: #include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
Chris@101: #include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
Chris@16: #include <boost/numeric/odeint/util/copy.hpp>
Chris@16: 
Chris@16: namespace boost {
Chris@16: namespace numeric {
Chris@16: namespace odeint {
Chris@16: 
Chris@16: template<
Chris@16: class State ,
Chris@16: class Value = double ,
Chris@16: class Deriv = State ,
Chris@16: class Time = Value ,
Chris@101: class Algebra = typename algebra_dispatcher< State >::algebra_type ,
Chris@101: class Operations = typename operations_dispatcher< State >::operations_type ,
Chris@16: class Resizer = initially_resizer
Chris@16: >
Chris@16: #ifndef DOXYGEN_SKIP
Chris@16: class modified_midpoint
Chris@16: : public explicit_stepper_base<
Chris@16:   modified_midpoint< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
Chris@16:   2 , State , Value , Deriv , Time , Algebra , Operations , Resizer >
Chris@16: #else
Chris@16: class modified_midpoint : public explicit_stepper_base
Chris@16: #endif
Chris@16: {
Chris@16: 
Chris@16: public :
Chris@16: 
Chris@16:     typedef explicit_stepper_base<
Chris@16:     modified_midpoint< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
Chris@16:     2 , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_base_type;
Chris@16: 
Chris@16:     typedef typename stepper_base_type::state_type state_type;
Chris@16:     typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
Chris@16:     typedef typename stepper_base_type::value_type value_type;
Chris@16:     typedef typename stepper_base_type::deriv_type deriv_type;
Chris@16:     typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
Chris@16:     typedef typename stepper_base_type::time_type time_type;
Chris@16:     typedef typename stepper_base_type::algebra_type algebra_type;
Chris@16:     typedef typename stepper_base_type::operations_type operations_type;
Chris@16:     typedef typename stepper_base_type::resizer_type resizer_type;
Chris@16:     typedef typename stepper_base_type::stepper_type stepper_type;
Chris@16: 
Chris@16: 
Chris@16:     modified_midpoint( unsigned short steps = 2 , const algebra_type &algebra = algebra_type() )
Chris@16:     : stepper_base_type( algebra ) , m_steps( steps )
Chris@16:     { }
Chris@16: 
Chris@16:     template< class System , class StateIn , class DerivIn , class StateOut >
Chris@16:     void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
Chris@16:     {
Chris@16:         static const value_type val1 = static_cast< value_type >( 1 );
Chris@16:         static const value_type val05 = static_cast< value_type >( 1 ) / static_cast< value_type >( 2 );
Chris@16: 
Chris@16:         m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) );
Chris@16: 
Chris@16:         const time_type h = dt /  static_cast<value_type>( m_steps );
Chris@16:         const time_type h2 = static_cast<value_type>(2) * h;
Chris@16: 
Chris@16:         typename odeint::unwrap_reference< System >::type &sys = system;
Chris@16: 
Chris@16:         time_type th = t + h;
Chris@16: 
Chris@16:         // m_x1 = x + h*dxdt
Chris@16:         stepper_base_type::m_algebra.for_each3( m_x1.m_v , in , dxdt ,
Chris@16:                 typename operations_type::template scale_sum2< value_type , time_type >( val1 , h ) );
Chris@16: 
Chris@16:         sys( m_x1.m_v , m_dxdt.m_v , th );
Chris@16: 
Chris@16:         boost::numeric::odeint::copy( in , m_x0.m_v );
Chris@16: 
Chris@16:         unsigned short i = 1;
Chris@16:         while( i != m_steps )
Chris@16:         {
Chris@16:             // general step
Chris@16:             //tmp = m_x1; m_x1 = m_x0 + h2*m_dxdt; m_x0 = tmp
Chris@16:             stepper_base_type::m_algebra.for_each3( m_x1.m_v , m_x0.m_v , m_dxdt.m_v ,
Chris@16:                     typename operations_type::template scale_sum_swap2< value_type , time_type >( val1 , h2 ) );
Chris@16:             th += h;
Chris@16:             sys( m_x1.m_v , m_dxdt.m_v , th);
Chris@16:             i++;
Chris@16:         }
Chris@16: 
Chris@16:         // last step
Chris@16:         // x = 0.5*( m_x0 + m_x1 + h*m_dxdt )
Chris@16:         stepper_base_type::m_algebra.for_each4( out , m_x0.m_v , m_x1.m_v , m_dxdt.m_v ,
Chris@16:                 typename operations_type::template scale_sum3< value_type , value_type , time_type >( val05 , val05 , val05*h ) );
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16:     void set_steps( unsigned short steps )
Chris@16:     {   m_steps = steps; }
Chris@16: 
Chris@16: 
Chris@16:     unsigned short steps( void ) const
Chris@16:     {   return m_steps; }
Chris@16: 
Chris@16: 
Chris@16:     template< class StateIn >
Chris@16:     void adjust_size( const StateIn &x )
Chris@16:     {
Chris@16:         resize_impl( x );
Chris@16:         stepper_base_type::adjust_size( x );
Chris@16:     }
Chris@16: 
Chris@16: private:
Chris@16: 
Chris@16:     template< class StateIn >
Chris@16:     bool resize_impl( const StateIn &x )
Chris@16:     {
Chris@16:         bool resized( false );
Chris@16:         resized |= adjust_size_by_resizeability( m_x0 , x , typename is_resizeable<state_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
Chris@16:         return resized;
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16:     unsigned short m_steps;
Chris@16: 
Chris@16:     resizer_type m_resizer;
Chris@16: 
Chris@16:     wrapped_state_type m_x0;
Chris@16:     wrapped_state_type m_x1;
Chris@16:     wrapped_deriv_type m_dxdt;
Chris@16: 
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: /* Modified midpoint which stores derivatives and state at dt/2 in some external storage for later usage in dense output calculation
Chris@16:  * This Stepper is for use in Bulirsch Stoer only. It DOES NOT meet any stepper concept.
Chris@16:  */
Chris@16: template<
Chris@16: class State ,
Chris@16: class Value = double ,
Chris@16: class Deriv = State ,
Chris@16: class Time = Value ,
Chris@101: class Algebra = typename algebra_dispatcher< State >::algebra_type ,
Chris@101: class Operations = typename operations_dispatcher< State >::operations_type ,
Chris@16: class Resizer = initially_resizer
Chris@16: >
Chris@16: class modified_midpoint_dense_out
Chris@16: {
Chris@16: 
Chris@16: public :
Chris@16: 
Chris@16:     typedef State state_type;
Chris@16:     typedef Value value_type;
Chris@16:     typedef Deriv deriv_type;
Chris@16:     typedef Time time_type;
Chris@16:     typedef Algebra algebra_type;
Chris@16:     typedef Operations operations_type;
Chris@16:     typedef Resizer resizer_type;
Chris@16:     typedef state_wrapper< state_type > wrapped_state_type;
Chris@16:     typedef state_wrapper< deriv_type > wrapped_deriv_type;
Chris@16: 
Chris@16:     typedef modified_midpoint_dense_out< State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_type;
Chris@16:     typedef std::vector< wrapped_deriv_type > deriv_table_type;
Chris@16: 
Chris@16:     modified_midpoint_dense_out( unsigned short steps = 2 , const algebra_type &algebra = algebra_type() )
Chris@16:     : m_algebra( algebra ) , m_steps( steps )
Chris@16:     { }
Chris@16: 
Chris@16:     /*
Chris@16:      * performs a modified midpoint step with m_steps intermediate points
Chris@16:      * stores approximation for x(t+dt/2) in x_mp and all evaluated function results in derivs
Chris@16:      *
Chris@16:      */
Chris@16: 
Chris@16:     template< class System , class StateIn , class DerivIn , class StateOut >
Chris@16:     void do_step( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt ,
Chris@16:             state_type &x_mp , deriv_table_type &derivs )
Chris@16:     {
Chris@16: 
Chris@16:         static const value_type val1 = static_cast< value_type >( 1 );
Chris@16:         static const value_type val05 = static_cast< value_type >( 1 ) / static_cast< value_type >( 2 );
Chris@16: 
Chris@16:         m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize< StateIn > , detail::ref( *this ) , detail::_1 ) );
Chris@16: 
Chris@16:         const time_type h = dt / static_cast<value_type>( m_steps );
Chris@16:         const time_type h2 = static_cast<value_type>( 2 ) * h;
Chris@16: 
Chris@16:         typename odeint::unwrap_reference< System >::type &sys = system;
Chris@16: 
Chris@16:         time_type th = t + h;
Chris@16: 
Chris@16:         // m_x1 = x + h*dxdt
Chris@16:         m_algebra.for_each3( m_x1.m_v , in , dxdt ,
Chris@16:                 typename operations_type::template scale_sum2< value_type , time_type >( val1 , h ) );
Chris@16: 
Chris@16:         if( m_steps == 2 )
Chris@16:             // result of first step already gives approximation at the center of the interval
Chris@16:             boost::numeric::odeint::copy( m_x1.m_v , x_mp );
Chris@16: 
Chris@16:         sys( m_x1.m_v , derivs[0].m_v , th );
Chris@16: 
Chris@16:         boost::numeric::odeint::copy( in , m_x0.m_v );
Chris@16: 
Chris@16:         unsigned short i = 1;
Chris@16:         while( i != m_steps )
Chris@16:         {
Chris@16:             // general step
Chris@16:             //tmp = m_x1; m_x1 = m_x0 + h2*m_dxdt; m_x0 = tmp
Chris@16:             m_algebra.for_each3( m_x1.m_v , m_x0.m_v , derivs[i-1].m_v ,
Chris@16:                     typename operations_type::template scale_sum_swap2< value_type , time_type >( val1 , h2 ) );
Chris@16:             if( i == m_steps/2-1 )
Chris@16:                 // save approximation at the center of the interval
Chris@16:                 boost::numeric::odeint::copy( m_x1.m_v , x_mp );
Chris@16: 
Chris@16:             th += h;
Chris@16:             sys( m_x1.m_v , derivs[i].m_v , th);
Chris@16:             i++;
Chris@16:         }
Chris@16: 
Chris@16:         // last step
Chris@16:         // x = 0.5*( m_x0 + m_x1 + h*m_dxdt )
Chris@16:         m_algebra.for_each4( out , m_x0.m_v , m_x1.m_v , derivs[m_steps-1].m_v ,
Chris@16:                 typename operations_type::template scale_sum3< value_type , value_type , time_type >( val05 , val05 , val05*h ) );
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16:     void set_steps( unsigned short steps )
Chris@16:     {   m_steps = steps; }
Chris@16: 
Chris@16: 
Chris@16:     unsigned short steps( void ) const
Chris@16:     {   return m_steps; }
Chris@16: 
Chris@16: 
Chris@16:     template< class StateIn >
Chris@16:     bool resize( const StateIn &x )
Chris@16:     {
Chris@16:         bool resized( false );
Chris@16:         resized |= adjust_size_by_resizeability( m_x0 , x , typename is_resizeable<state_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() );
Chris@16:         return resized;
Chris@16:     }
Chris@16: 
Chris@16:     template< class StateIn >
Chris@16:     void adjust_size( const StateIn &x )
Chris@16:     {
Chris@16:         resize( x );
Chris@16:     }
Chris@16: 
Chris@16: private:
Chris@16: 
Chris@16:     algebra_type m_algebra;
Chris@16: 
Chris@16:     unsigned short m_steps;
Chris@16: 
Chris@16:     resizer_type m_resizer;
Chris@16: 
Chris@16:     wrapped_state_type m_x0;
Chris@16:     wrapped_state_type m_x1;
Chris@16: 
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: /********** DOXYGEN ***********/
Chris@16: 
Chris@16: /**
Chris@16:  * \class modified_midpoint
Chris@16:  *
Chris@16:  * Implementation of the modified midpoint method with a configurable 
Chris@16:  * number of intermediate steps. This class is used by the Bulirsch-Stoer
Chris@16:  * algorithm and is not meant for direct usage.
Chris@16:  */
Chris@16: 
Chris@16: 
Chris@16: /**
Chris@16:  * \class modified_midpoint_dense_out
Chris@16:  *
Chris@16:  * Implementation of the modified midpoint method with a configurable 
Chris@16:  * number of intermediate steps. This class is used by the dense output
Chris@16:  * Bulirsch-Stoer algorithm and is not meant for direct usage.
Chris@16:  * \note This stepper is for internal use only and does not meet 
Chris@16:  * any stepper concept.
Chris@16:  */
Chris@16: 
Chris@16: 
Chris@16: }
Chris@16: }
Chris@16: }
Chris@16: 
Chris@16: #endif // BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED